Wave transmission network



ZJOZQMM Jam 28, 1936 H. w. BODE WAVE TRANSMISSION NETWORK 5 Sheets-Sheet 1 Filed Jan. 51, 1934 //v ve/v TOR 0 FREQUENCY 1 i ATTORNEY J2 FREQUENCY Jam. 28,

ATTENUATION H. W. BODE ZQZSMM WAVE TRANSMISSION NETWORK Filed Jan. 51, 1954 FIG/.2

FREQUENCY 3 Sheets-Sheet 2 FIG/3 FREQUENCY ATTENUATION FIG. /5

INVENTOR H. W. 5005 A 7' TOR/VE V ZWQGM aFan, 28, 1936. H. W. BODE WAVE TRANSMISSION NETWORK Filed Jan. 51, 1934 3 Sheets-Sheet 3 FIG. 2/ F FREQUENCY FIG. 28

lNl/ENTOR HWBODE 5y Z ATTORNEY Patented Jan. 28, 1936 UNETE STAT Ffiiihii iil' FFEQE Bell Teiephone Laboratories, incorporated,

New York, N. 1 a corporation of New York Application January 31, 1934, Serial No. 703,975

30 Ciaims.

This invention relates to wave transmission networks and more particulariyto means within such a network for making its attenuation characteristic uniform throughout the transmission range.

The principal object of the invention is to make the attenuation of a transmission network uniform in the transmission band.

A feature of the invention is a wave filter of the ladder type in which a dissipative impedance branch is added in series or in shunt in order to equalize the attenuation of the filter throughout its transmission band.

It is well known that the attenuation of any physically realizable wave filter of the ladder type is not uniform with frequency throughout the transmission band but, in general, increases in magnitude as the cut-off frequencies are approached. This attenuation distortion is due in part to the energy dissipation inherent in the reactance elements of which the filter is composed. I-Ieretofore the practice has been to employ separate attenuation equalizers to compensate for the distortion. In accordance with the 25 present invention, however, this attenuation distortion is compensated by means within the filter and the network is thus made self-equalizing. For this purpose a dissipative impedance branch is added in shunt between two mid-series termi- 30 nated sections of the filter, or is inserted in series between two midshunt terminated sections. The added impedance branch may consist simply of an ohmic resistance or it may comprise both resistance and reactance elements in combination.

The nature of the invention will be more fully understood from the following detailed description and by reference to the accompanying drawings, of which Fig. 1 illustrates diagrammatically the application of the invention to a ladder type transmission network in which a dissipative impedance branch is inserted in shunt between two midseries terminated half-sections;

Fig. 2 is an alternative configuration for the network of Fig. 1 in which a dissipative impedance branch is added in series between two midshunt terminated half-sections;

Fig. 3 represents a network of the type shown in 1 in which the inserted impedance is a conductance;

Fig. 4 illustrates the application of the invention to a low-pass wave filter of the constant-7c yp Fig. 5 gives the type of attenuation characteristic obtainable from the network of Fig. 4;

(ill. 178-44) Fig. 6 illustrates the type of correction curves obtainable when the invention is applied to a wave filter of the m-derived type;

7 represents a network of the type shown in Fig. 2 in which the added impedance is a resistance;

Fig. 8 is an alternative configuration for the network of Fig. 4;

Figs. 9 and 10 show the application of the invention to symmetrical band-pass filters of the constant-k type;

Fig. 11 gives typical attenuation characteristics obtainable from the filters shown in Figs. 9 and 10;

Figs. 12 and 14 represent unsymmetrical bandpass filters embodying the invention;

Fig. 13 gives the type of correction characteristic obtainable from the filtersof Figs. 12 and 14;

Figs. 15 and 16 show alternative configurations for the networks of Figs. 12 and 14, respectively;

Figs. 17, 18 and 19 illustrate modified forms of the invention in which mutual inductance is employed;

Figs. 20, 21 and 22 give the equivalent electrical circuits of the networks shown respectively in Figs. 17, 18 and 19;

Fig. 23 shows the application of the invention to a network in which only a portion of the series impedance branch is bisected;

Fig. 24 represents the electrical equivalent of the filter of Fig. 23;

Fig. 25 illustrates correction characteristics to which reference is made in describing a modification of the invention;

Fig. 26 shows a modification of the invention in which an anti-resonant circuit is introduced in series with the equalizing conductance;

Fig. 27 gives the type of attenuation characteristics attainable with the network of Fig. 26;

Fig. 28 is an alternative configuration for the filter section of Fig. 26; and

Figs. 29 and 30 show modifications, respectively, of the networks of Figs. 26 and 28.

Fig. 1 represents diagrammatically a wave filter of the ladder type, that is, one having impedances Z1 in series with the line and impedances Z2 alternately disposed in shunt with the line. The network has a pair of input terminals I I, I2 and a pair of output terminals l3, l4 by means of which the filter may be connected between two sections of transmission line or to other apparatus of suitable impedance. For the sake of simplicity the network is illustrated in the unbalanced form, but the invention is equally applicable to a balanced structure. The path bel the transmission band. The added impedance 'otherwise fixed in potential.

branch ZX is connectedbetween the, junction point l5 of the pair of equal series impedances and a point It in the grounded side of the filter,

for the purpose of equalizing the attenuation in branch Zxmay consist ofa resistance only, or it may comprise both resistance and reactance elements in combination. How the character and a magnitude of ZX are determined is fully explained.

hereinafter. I i

Fig. 2 represents an alternative configuration from which the same results'may be obtainedas from the network, of Fig.1.v Fig.- 2 shows a dissipative impedance branch Zy connected in series between two mid-shunt terminated half-sections of aladdertypenetwork. The impedance 3 Zy may be simply an ohmic resistance or it may be made up of resistance and reactance elements. In general, the impedances Zx and. Zy will have an inverse relationship to each other.

' a 'If the impedance ZX of Fig; l is a resistance only, the network will be as shown in Fig. 3, whereG represents theconductan'ce of the inserted; equalizing branch; 7 The efiect upon the attenuation of the network caused by introducing s the conductance Gwill now he considered. As-

suming that the load impedances between which the network is connected match its terminal impedances then, with the branch G disconnected, the impedance seen in either direction' from G r is the mid-series image impedance Z1 *of the.

filter. Therefore; the total admittance of the cir-' cuit'taken at the points l5,' l6 with the branch where; is the base of the Napierian system of 7 when dis inserted, the admittance at this point By standard formulae, the insertion loss 05in nepers caused by the introduction ofithe branch G may be found from the expression logarithms. When 0 is small I V e i 1 +0 and, therefore, small losses are given with sufiicient accuracy by the equation r which is obtained for substiuting for e in Equation (l).' Since G is a constant it is evident that the. insertion of the equalizing branch introduces a loss which varies with frequency and- '.isdirctlyproporticnal to'the mid-series image impedance Zr of the network.

n the unmodified network is s wsve filter (as the low-pass; constant-Ietype described in United States Patent No. 1,22'7,113', to C reorge A. Camp- In accordresistance, in the same bell,'issued May 22, 1917 the circuit shown in Fig. 4 will be obtained when the impedance branch G is inserted. The mid-series imageimpedance Z: of such a filter is'resistive throughout 7 the transmission band, starting at a finite'value cut-off, and is reactive outside of the band, starting at zero at the cut-off and increasing to an infinite value at infinite frequency. The loss intro; duced by the insertion of the conductance'G;

since it, is proportional to Z1, will therefore be of the type shown diagrammatically by curve I! of Fig. 5, where f0 indicates thecut-off frequency. This, however, is well adapted for equalizing the usual loss curve of the uncorrected filter, illusat zero frequency and falling 01f to zero at the V trated by curve l8 of Fig. 5, which is small at zero frequency'and. increases as the cut-off is approached. Theattenuation of the filter after 7 the equalizing branch is. inserted, which is the summation of curves H and i8, is shown by curve 19 of Fig. 5. It" will be noted that the attenua tion is substantially uniform throughout the transmission band and that in the attenuating.

range the discrimination is improved. 7,

For purposes of illustration this case .will be retical analysis that, except at frequencies very close to the cut-ofi,.the attenuation 7A0 in nepers treated more precisely. It can be shown by theointroduced by 1; sections of anunmodified constant-Zc, low-pass'fiiter in its transmission band 'is given apprcxirnately by the equation 1 n I V V i' zwf 'f /r-x where it: represents the cut-off frequency,

and

. 'representsthe ratio of the resistance of a typical 7 It followsfrom'Equation (2) that the insertion loss A1 of the equalizing notation, is given by the coil to its inductance.

expression V where Z0 is the zero frequency value of; the image impedance. modified'n'etwork'in the transmitting band consequently becomes 1 V The total attenuation. A2 of the we 1 Now the expression for A0 given by Equation 7 q (3) has the same algebraic form as the expres- 'sionfor the mid-shunti image impedance of a constant-7c, low-pass filter provided we let the constant I j V I n I arr. L

impedance.

m-derived type} asdescribed by O. J. Zobelin I represent the zero frequency value of the image V The expression given'by Equation (5) on the other hand, is similar to the expres sion fcr'an image'impedance of the mid-shunt;

United, Stat-esPatent No. 1,538,964, issued May 1 2 6, 1925, provided we setthe constant V V n r G'Z "216.1 2

equal to the zero frequency value of the image impedance and set the constant mathematically analogous to the improvement in the constancy of the filter image impedance equal to 1-m which Zobel obtains by m-derivation in the above -mentioned patent. In particular, Zobel finds that the value m=0.6 leads to a very nearly constant characteristic. On account of the relation mentioned above, if a similar constancy in the attenuation throughout the transmission band is to be secured, the conductance G in the present case must be given the following value If the unmodified filter is of the low-pass, mderived type described in the Zobel patent mentioned above, a variety of other correction curves may be obtained, of the form illustrated by curves 2|, 22 and 23 of Fig. 6, which give the loss introduced by the insertion of a conductance G in the network shown in Fig. 3. Curve 20, also given in Fig. 6 for the sake of comparison, shows the correction obtainable when a constant-k section is used. All of these curves are more or less adapted to equalize the normal filter attenuation characteristic and, therefore, by properly combining them in a multi-section composite filter a high degree of uniformity may be attained for the attenuation of the filter in its transmission band. Still more perfect equalization may be secured, in some instances, by the use of the double m-derived filter sections described in United States Patent No. 1,850,146 to Zobel, issued March 22, 1932. The applicability of the invention is not restricted to any particular type of ladder section and the foregoing are mentioned only by way of illustration.

If the impedance Z of Fig. 2 is a simple ohmic resistance of value R the resulting network will be as shown in Fig. '7. Following the same steps taken above in the analysis of the circuit of Fig.

3, before the branch R, is inserted the impedance taken at this point is equal to twice the midshunt image impedance Z1 of the network. After R is inserted, the impedance is R+2Z1'. Hence, the insertion loss caused by the introduction of the resistance R is given by the equation R+2Z R e ZZII 1+2ZII Or, where small losses are involved,

If .R is constant the loss introduced by the insertion of the equalizing branch is thus seen to be inversely proportional to the mid-shunt image impedance Z1 of the network. If the unmodified network is a low-pass, constant-k type filter as shown in Fig. 8 the correction curve obtainable by the addition of R will be of the type given by curve ll of Fig. 5, which is the same as that resulting from the introduction of the branch G in the network of Fig. 4. It is thus apparent that the network of Fig. 8 is the electrical equivalent of the one shown in Fig. 4. The two configurations may be used interchangeably, and an equalized characteristic of the type shown by curve 19 of Fig. may be obtained from either network.

For symmetrical band-pass filters of the constant-k type the analysis is the same as given above. The resulting networks are given in Figs. 9 and 10, which are equivalent circuits. A typical attenuation characteristic between the cut-off frequencies f1 and f2 of the uncorrected filter is given diagrammatically by curve 24 of Fig. 11, the loss added by the introduction of G or R is given by curve 25 and the resultant equalized characteristic by curve 26.

In the case of unsymmetrical band-pass filters there may be obtained a correction curve which either increases or decreases with frequency. For example, the mid-series image impedance of the band-pass filter shown in Fig. 12 decreases with frequency, and therefore the loss caused by inserting the conductance G will be of the form given by curve 21 of Fig. 13. This type of correction curve is well adapted to equalize the attenuation of a filter which has a deficiency of loss on the lower side of the band. By using the type of section shown in Fig. 14 the other type of dissymmetry, given by curve 28 of Fig. 13, is secured. Figs. 15 and 16 show alternative configurations for the networks of Figs. 12 and 14, respectively.

The cost of the above described method of making filters self-equalizing by the introduction of a dissipative impedance branch can be measured by the increase in the number of component elements which follows from the necessity of bisecting one of the series or one of the shunt branches of the original structure. Under ordinary circumstances this cost is not large, but in accordance with a modified form of the invention, it can be made still smaller by the introduction of mutual inductance between certain of the bisected inductances. Several illustrations of this modification are furnished by the networks of Figs. 1'7, 18 and 19, the equivalent circuits of which are shown, respectively, in Figs. 20, 21 and 22.

Fig. 17, for example, shows an equalized lowpass filter of the constant-k type in which the bisected series inductance, instead of being built as two separate coils, is built as a single, twowinding transformer, comprising the two equal inductances L, Lcoupled by mutual inductance M. The equivalent circuit for this network is given in Fig. which, it will be noted, is of the same form as the configuration of Fig. 4., except that a negative inductance in magnitude equal to M is introduced in series with the equalizing conductance G.

Fig. 18 shows how the invention may be applied to a qr-SGCtlOll of any ladder type network without the necessity of bisecting any of the impedance branches of the original structure. A transformer having two equal windings L, L of large selfinductance coupled series-aiding by mutual inductance M equal substantially to L is shunted across the terminals of the series impedance branch Z1, and the conductance G is connected between the junction point of the transformer windings and the grounded side of the network. The electrical equivalent of the circuit of Fig. 18 is shown in Fig. 21, in which an equalizing branch comprising a negative impedance equal in magnitude to AZ; in series with the conductance G is connected from the mid-point of the series v impedance branch to ground.

Fig. 19 illustrates a method of introducing an equalizing branch in a T-section without bisecting any of the branches. A two-winding transformer similar to the one described above in connection with Fig. 18 is placed in series between the two series impedances Zl, the equalizing resistance R is bridged across the outer terminals of the f The equivalent electrical c cuit, as shown in Fig.

22, comprises the resista R in parallel with a negative impedance equai in magnitude to 422.,

the combination being connected in series between the two halves of the bisected shunt branch. If the series impedance branch of the network to be equalized comprises two or more paths con nected in parallel, it may be found convenient to bisectonly one of these paths, in which case no mutual inductance need be used. Anfexamplc is given in Fig. 23, in which the original struce tureisa double m-derived, low-pass filter section of the type shown in Fig. 6a of United States Pat ,ent No. 1,850,146 to Zobel, issued March 22, 1932.

The series branch comprises an inductance L1 in parallel with a path comprising an inductance Lzconnected in series with a capacitance C. In accordance with the invention, the inductance L1 is divided into two equal parts and the conductance G is connected from the common terminal the grounded side of the network. The equiv-' alent electrical circuit is given in Fig. 24 where it'is'seen that the equalizing branch is in efi'ect connected between the mid-point of the series branch and ground, but a complex reactance is also introduced in series with G.

, The feasibility of adopting the expedients illustrated by Figs. l7, i8, 19 and 20 depends upon the .fact that, if the insertion loss introduced by the equalization is small, the equalizing conductance G, when the equalization is performed in accordance with Fig. 3, or the equalizing resistance B, when the equalizationis performed in accordance with Fig. '7, willalso be small. It follows that a small impedance added in series with G of Fig. 3, or a large impedance added in parallel with R of'Fig. '7, will not appreciably aifect the equalization procurable. circuits shown in Figs. 29, 21 and 24' is of the form shown in Fig. 3 comprising a bisected series branch, except that an impedance is introduced in series with the conductance G. Since the magnitude of these added impedances in each instance is, only fractional part of the normal parallelling impedance'is iour jtimes as largeias the normal shunt impedance branch of the filter,

'1 and therefore its eiiect upontiie equalization shunt with'it, is, relatively small.

secured is not seriously detrimental. V

' The argument presented above is valid only be-. cause the impedance added in series with the equalizing resistance, or the admittance added in This suggests a further modification of the invention, in which a large impedance or admittance. is introduced in 7 order to improve the equalization. For example, the desired correction curve may be the one given Each of the equivalent by curve 29 of Fig. 25 while the one obtainable is given by curve of the same figure. Considering the network of Fig. 4, it willbe noted that the equalizing branch G is essentially a leak divert ing current from the further. portions of the structure. It diverts less current near the cutifbecause the image impedance of the filter de I creases as thecutoff r"requency is approached. The branch G would divert still less current in this region if, instead of remaining constant, its impedance increases with frequency. This desired result is accomplished by adding an inductanceor an anti-resonant circuit in series with G, which serves to diminish themagnitud or" the leak near the cut-off without appreciable effect at low frequencies. An example is shown in Fig. 26, where the equalizing branch, consisting of the conductance G in' series with the series terminals of a constant-k, low-pass'filter section.

i'stic obtainable when the equalizing branchis a simple conductance G, and curve'33'is the char- ;acteristic obtained when the anti-resonant circuit is added in series with G. Theunit. of attenuation is taken as the coefiicient.

.. n j fi, L

secured. 1- I I u V The inverse configuration of the network of Fig. 26 isfgiven in Fig; in which'the equalizing branch comprises 'ar'esist'ance R shunted by a resonant path consisting of. an inductance L' in shunt impedance branch of the filter. The char; acteristic obtainable with the filter of Fig; 28 is the same as the one shown in Fig. 27 by curve In some instances the'capacitance C of Fig.

may be omitted, and likewise in some casesthe inductance L of Fig. 23rnay be left out, butthe degree of equalization will be somewhat impaired The resulting networks are 7 shown, respectively; in Figs. 29 and 30. I What is claimed is:

this is done.

1. In a wave transmissionnetwork'oi the ladder type having impedance branches in series.

with the line and alternately disposed impedance branches in shunt therewith, the attenuation of said filter in its transmission hand varying with frequency due to thedissipation inherent in the' reactance elements comprising said network, two

impedance branches, a third impedance branch V interposed therebetween, and internal means for equalizing thetransmission characteristic of said' network in its transmission band, said means comprising an additional dissipative impedance tioned with respect to the image impedance. of

]said network at the mid-point of's aid third Curve 3!. of Fig. 2'? shows the attenua: tion characteristic of the filter'of Fig. 26 without j equalization, curve 32 represents the' characteranti-resonant'loop'made up'of the inductance L and the capacitance C, is inserted at. the midof Equation (3) and represents the attenuation 1 of the unequalizedfilter at zero frequency; It will be observed that the introduction of the anti-resonant circuit produces an improvement of about four to one in the quality of equalization branch so that the entire network has a'uniform I transmission V .2. In a wave transmission network of the ladcharacteristicin said transmission with frequency due to the dissipation inherent in the reactance elements comprising said network, two shunt impedance branches, an interposed series impedance branch, and energy absorbing means within said network for equalizing its transmission characteristic in the transmission band, said means comprising a conductance connected effectively between an intermediate point in said series branch and the other side of the line, and said conductance being so proportioned with respect to the image impedance of said network at said intermediate point or" connection that the entire network has a uniform transmission characteristic in said transmission band.

3. In awave transmission network of the ladder type having impedance branches in series with the line and alternately disposed impedance branches in shunt therewith, the attenuation of said network in its transmission band varying with frequency due to the dissipation inherent in the reactance elements comprising said network, two shunt impedance branches, an interposed series impedance branch, and an additional dissipative impedance branch inserted for the purpose of equalizing the transmission characteristic of said network in its transmission band, said additional branch being inserted effectively at the mid-point of said series branch and being so proportioned with respect to the image impedance of said network at said mid-point that the attenuation of the network as a whole is made uniform in said transmission band.

4. In a ladder type wave filter having an attenuation characteristic which varies with frequency in the transmission band due to the dissipation inherent in the reactance elements comprising said filter, two series impedance branches, an interposed shunt impedance branch, and means within said filter for making its attenuation uniform in the transmission band, said means comprising a resistance connected in series with the line effectively at an intermediate point in said shunt branch, said resistance being so proportioned with respect to the image impedance of said filter at said intermediate point that the attenuation of said filter as a whole is made uniform in its transmission band.

5. In a ladder type wave filter the attenuation of which Varies with frequency in the transmission band due to the dissipation inherent in the reactance elements comprising said filter, two series impedance branches, an interposed shunt impedance branch, and an additional dissipative impedance branch introduced for the purpose of making the attenuation of said filter uniform in the transmission band, said additional branch being connected in series with the line effectively at the mid-point of said shunt branch and being so proportioned with respect to the image impedance of said filter at said mid-point that the attenuation of the filter as a whole is made uniform in said transmission band.

6. In a ladder type wave filter having series impedance branches and alternately disposed shunt impedance branches, and having an attenuation characteristic which in the transmission band varies with frequency due to the dissipation inherent in the reactance elements comprising said filter, two impedance branches of one kind, a third impedance branch of the other kind interposed therebetween, and energy absorbing means within said filter for compensating the attenuation distortion due to said dissipation comprising a resistance element introduced into said filter effectively at the mid-point of said third branch, the magnitude of said resistance element being so proportioned with respect to the image impedance of said filter at the midpoint of said third branch that the attenuation of said filter as a whole is made uniform in said transmission band.

i. In a wave filter of the type having imped- 1 ance branches in series with the line and alternately disposed impedance branches in shunt with the line, the attenuation characteristic of said filter in its transmission band varying with r'requency due to the dissipation inherent in the reactance elements comprising said filter, two shunt impedance branches, a series impedance branch interposed therebetween, and an added dissipative impedance branch connected between the mid-point of said series impedance branch and the other side of the line.

8. In a wave filter of the type having impedance branches in series with the line and alternately disposed impedance branches in shunt with the line, said filter having an attenuation characteristic which varies in the transmission band due to the energy dissipation inherent in the reactance elements comprising said filter, two series impedance branches, a shunt impedance branch interposed therebetween, and an added dissipative impedance branch connected in series with the line at a point between said two shunt impedance branches.

9. In a wave transmission network of the ladder type having an attenuation characteristic which in the transmission band varies with frequency due to the energy dissipation inherent in the reactance elements comprising said network, two mid-series terminated half-sections connected together at their mid-series ends, and a dissipative impedance branch inserted in shunt with the line between said two mid-series terminated half-sections, the impedance of said dissipative branch being so proportioned with respect to the mid-series image impedance of said network that the attenuation of the entire network is equalized in said transmission band.

. 10. In a wave transmission network of the ladder type having an attenuation characteristic which in the transmission band varies with frequency due to the energy dissipation inherent in the reactance elements comprising said network, two mid-shunt terminated half-sections connected together at their mid-shunt ends, and a dissipative impedance branch inserted in series with the line between said two mid-shunt terminated half-sections, the impedance of said dissipative branch being so proportioned with respect to the mid-shunt image impedance of said network that the attenuation of the entire network is equalized in said transmission band.

11. In a wave filter of the ladder type having an attenuation characteristic which varies in the transmission band due to the dissipation inherent in the reactance elements of said filter, two mid-series terminated half-sections connected together at their mid-series ends, and a conductance connected in shunt with the line at a point between said two mid-series terminated half-sections, the magnitude of said conductance being so proportioned with respect to the midseries image impedance of said filter that the attenuation of the entire combination is equalized in said transmission band.

V 12.'In a wave filter of the ladder type having an attenuation characteristic which varies in the transmission'band due to the dissipation inherent in the reactance elements comprising said filter, 7

I attenuation characteristic which varies in the transmission band due to the dissipation inherent in the reactance elements comprising said filter,-two mid-series terminated half-sections connected' together at their mid-series ends, an

an equalizing impedance branch connected in shunt with the line at a point between said two mid-series terminated half-sections, said equalizing branch comprising resistance and reactance elements in combination, and the impedance of said equalizing branch being so proportioned with respect to the mid-series image impedance of said filter that the attenuation of the entire combination is equalized in said transmission band.

14;. In a ladder type wave filter having an attenuation characteristic which varies in the transmission band due to the dissipation inherent in the reactance elements comprising said filter, two mid-shunt terminated half-sections connected together at their mid-shunt ends, and

an equalizing impedance branch connected in series with the line at a point between said two mid-shunt terminated half-sections, said equalizing branch comprising resistance and reactance elements in combination, and the impedance of said equalizing branch being so proportioned with respect to the mid-shunt image impedance of said filter that the attenuation of the entire combination is equalized in said transmission band.

15.. In a ladder type. wave filter having an attenuation characteristic which varies in the a transmission band due to the dissipation inherent in the reactance elements comprising said filter, two mid-series terminated half-sections connected together at their mid-series ends, and an impedance branch comprising a conductance in series with an inductance, said branch shunting the line at a point between said two midseries terminated half-sections and the impedance of said branch being so proportioned with respect to the mid-series image impedance of said filter that the attenuation of the entire combination is equalized in said transmission band. 16. In a ladder type wave filter having an attenuation characteristic which varies in the transmission band due'to the dissipation inherent in the reactance elements comprising said filter, two mid-shunt terminated half-sections connected together at their mid-shunt ends, and an impedance branch comprising a'resistance in parallel with a capacitance, said branch being connected in series with the line'between said two mid-shunt terminated half-sections, and the impedance of said branch being so proportioned with respect to the mid-shunt image impedance of said filter that the attenuation of the entire combination is equalized in said transmission band.

17. In a wave filter of thetype having impede ance branches in series with the line andalternately dispose'd'impedance branches in shunt with the line, a'series impedance branch inter.-

'posed between two shunt impedance branches, a branch comprising a pair of equal inductances connected series aiding with unity coupling factor shunted around said series impedance branch,

and a'conductance connected between the common terminal of said pair of inductances and the other side of the line. a

18. In a wave filter of the type having impedance branches in series with the line and alternately disposed impedance branches in shunt with the line, a resistance connected in series between two adjacent series impedance branches of the filter, and a branch comprising a pairoi equal inductance-s connected series aiding with; unity coupling factor shunted aroundsaid resist ance, the intervening shunt impedance branch of the filter being connected between the com-v mon terminal of said pair of inductances and a the other side'of the line.

19. In a wave filter of the ladder type having an attenuation characteristic which varies in the transmission band due to the dissipation inherent in the reactance elements comprising said filter, two shunt impedance branches and an intervening series impedance branch, said series; impedance branch comprising a pair of equal,

inductances, inductively coupled, connected in series, and a conductance connected from the.

pacitances, the attenuation of said filter varying with frequency in the transmission'band due to.

the dissipation inherent in the reactance elements comprising said filter, a series impedance branch comprising two equal series inductances with mutual inductance therebetween, and a conductance connected between the common ter- ,7

minal of said pair of inductances and the other side of the filter, the magnitude of said cone. ductance being so proportioned with respect to the mid-series image impedance of said filter that a the'attenuation of the structure as a whole is equalized in said transmission band.

21. In a wave filter of the type having impedance branches inseries with the line and alternately disposed impedance branches in shunt .7

with the line, the attenuation of said filter varyto the dissipation inherent in the reactance elements comprising said filter, two shunt imped pedance branch connected between the mid-v I point of one of said parallel paths and the other side of the line, the impedance of said dissipa-.

- ing with frequency in the transmission band due tive branch being so proportioned with respect to the mid-series image impedance of said filter that the attenuation of the structure as a whole is equalized in said transmission band.

22. In a wave filter of the ladder type in which ent in the reactance elements of saidfilteni'two'vw shunt impedance branches, an intervening "series impedance branch, and a dissipative impedance branch connected in shunt with the line effectively at an intermediate point in said series branch, said dissipative branch comprising a resistance in series with an anti-resonant loop, and the impedance of said dissipative branch being so proportioned with respect to the image impedance of said filter at said intermediate point in said series branch that the attenuation of said filter is equalized in said transmission band.

23. In a wave filter of the ladder type having an attenuation characteristic which varies with frequency due to the dissipation inherent in the reactance elements comprising said filter, two series impedance branches, an interposed shunt impedance branch divided into two portions, and a dissipative impedance branch connected in series with the line between said two portions of said shunt branch, said dissipative branch comprising a resistance in parallel with a resonant path, and the impedance of said dissipative branch being so proportioned with respect to the image impedance of said filter at the point of division of said shunt branch that the attenuation of said filter is equalized in said transmission band.

24. In a ladder type wave filter comprising series impedance branches and alternately disposed shunt impedance branches and having attenuation distortion in the transmission band due to the energy dissipation inherent in the component reactance elements comprising said filter, two impedance branches of one kind, an interposed impedance branch of the other kind, and an additional dissipative impedance branch comprising resistance and reactance elements introduced into the filter structure at an intermediate point in said interposed impedance branch, the impedance of said additional branch being so proportioned with respect to the image impedance of said filter at said intermediate point that said attenuation distortion is substantially eliminated.

25. Ina ladder type wave filter having attenuation distortion in the transmission band due to the energy dissipation inherent in the component reactance elements comprising said filter, two series impedance branches, an intervening shunt impedance branch divided into two portions, and a dissipative series impedance branch introduced into the filter structure between said two portions of said shunt branch at a point where the image impedance characteristic of said filter has the same general shape in the transmission band as the uncompensated attenuation characteristic, whereby said attenuation distortion is substantially reduced.

26. In a ladder type wave filter having attenuation distortion in the transmission band due to the energy dissipation inherent in the component reactance elements comprising said filter, two shunt impedance branches, an interposed series impedance branch divided into two portions, and a dissipative shunt impedance branch introduced into the filter structure at the point of junction of said two portions of said series branch where the image impedance characteristic of the filter is approximately the converse of the uncompensated attenuation characteristic in the transmission band, whereby said attenuation distortion is substantially eliminated.

27. In a ladder type wave filter the attenuation of which varies in the transmission band due to the dissipation inherent in the reactance elements constituting said filter, two shunt impedance branches, an interposed series impedance branch, an additional dissipative shunt impedance branch, and means comprising two coupled inductances for connecting said dissipative impedance branch effectively, from an intermediate point in said series branch to the other side of the line.

28. In a ladder type wave filter the attenuation of which varies in the transmission band due to the dissipation inherent in the reactance elements constituting said filter, two series impedance branches, an intervening shunt impedance branch, an additional dissipative series impedance branch, and means comprising two coupled inductances for connecting said dissipative impedance branch into said filter effectively in series with the line between two portions of said shunt impedance branch.

29. In a wave filter of the type having impedance branches in series with the line and alternately disposed impedance branches in shunt with the line, the attenuation of said filter varying with frequency due to the dissipation inherent in the reactance elements comprising said filter, two impedance branches, a third impedance branch interposed therebetween, and internal means for increasing the attenuation of said filter in its transmission band, said means comprising an additional dissipative impedance branch inserted in said filter efiectively at an intermediate point in said third branch, the impedance ofsaid additional branch being so proportioned with respect to the image impedance of said filter at the point of insertion and also with respect to the difference between the attenuation curve of said filter and a desired attenuation curve that the combination gives said desired curve in the transmission band of said filter.

30. In a wave filter of the type having impedance branches in series with the direction of wave propagation and alternately disposed impedance branches in shunt therewith, the attenuation of said filter varying with frequency due to the dissipation inherent in the reactance elements comprising said filter, two impedance branches, a third impedance branch interposed therebetween, and an attenuation correcting branch introduced into said filter efiectively at an intermediate point in said third branch, said correcting branch comprising a dissipative impedance element, and the impedance of said correcting branch being so chosen with respect to the image impedance of said filter at the point of introduction that the attenuation of said filter supplemented by the attenuation introduced by said correcting branch provides an attenuation characteristic for the combination which is uniform throughout the transmission band of said filter.

HENDRIK W. BODE. 

